Parent
There are two forms of Parent we can play.
The Nurturing Parent is caring and concerned and often may appear as a mother-figure (though men can play it too). They seek to keep the Child contented, offering a safe haven and unconditional love to calm the Child's troubles.
The Controlling (or Critical) Parent, on the other hand, tries to make the Child do as the parent wants them to do, perhaps transferring values or beliefs or helping the Child to understand and live in society. They may also have negative intent, using the Child as a whipping-boy or worse.
Adult
the Adult in us is the 'grown up' rational person who talks reasonably and assertively, neither trying to control nor reacting aggressively towards others. The Adult is comfortable with themself and is, for many of us, our 'ideal self'.
Child
There are three types of Child we can play.
The Natural Child is largely un-self-aware and is characterized by the non-speech noises they make (yahoo, whee, etc.). They like playing and are open and vulnerable.
The cutely-named Little Professor is the curious and exploring Child who is always trying out new stuff (often much to their Controlling Parent's annoyance). Together with the Natural Child they make up the Free Child.
The Adaptive Child reacts to the world around them, either changing themselves to fit in or rebelling against the forces they feel.